Prove that

Given :

$3 x+2 y=12 \quad \ldots(1)$

$x-y+1=0 \quad \ldots(2)$

$x-y+1=0$

$\Rightarrow y=x+1 \quad \ldots(3)$

Substituting the value of $y$ in $(1)$, we get

$3 x+2(x+1)=12$

$\Rightarrow 3 x+2 x+2=12$

$\Rightarrow 5 x=12-2$

$\Rightarrow 5 x=10$

$\Rightarrow x=2 \quad \ldots(4)$

Substituting the value of $x$ in $(3)$, we get

$y=2+1=3$

Hence, $x=2$ and $y=3$.